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Oct 22, 2015 at 13:16 vote accept David Barnes
Oct 22, 2015 at 10:08 comment added user51223 To an inclusion of compact Lie groups $H<G$, a suitable transfer in the sense of Becker-Schultz as well as Mann-Miller-Miller, $t_H^G:BG^{ad_G+\alpha}\to BH^{ad_H+\alpha|_H}$ can be associated where $\alpha\to BG$ is some (virtual) vector bundle, and $ad_G$ is the adjoint bundle associated to the adjoint representation of $G$. Then, how far is the answer to the question ``to what extend does $t_H^G$ induce a surjection in homotopy groups/equivariant homotopy groups?'' from an answer to your question?
Oct 21, 2015 at 16:35 answer added Tyler Lawson timeline score: 8
Oct 21, 2015 at 11:34 comment added Tom Goodwillie You had better be clear as to what the weak equivalences are: do they induce equivalences on fixed-point spectra? But either way I don't believe 1 is true.
Oct 21, 2015 at 11:14 history asked David Barnes CC BY-SA 3.0